Analyzing earthquake clustering features by using stochastic reconstruction

Journal of Geophysical Research: Solid Earth

Volumn 109, Issue 5, 2004, Pages

  Zhuang, Jiancang ^a   Ogata, Yosihiko ^a   Vere Jones, David ^b  

^a INSTITUTE OF STATISTICAL MATHEMATICS   (Japan)

^b VICTORIA UNIVERSITY OF WELLINGTON   (New Zealand)

Author keywords

Afterschock; ETAS model; Point process; Stochastic declustering; Stochastic reconstruction; Triggered seismicity

Indexed keywords

AFTERSHOCK; CLASSIFICATION; EARTHQUAKE; STOCHASTICITY;

EID: 4644316414     PISSN: 21699313     EISSN: 21699356     Source Type: Journal    
DOI: 10.1029/2003JB002879     Document Type: Article

References (42)

1. Choi, E., and P. Hall (1999), Nonparametric approach to analysis of spacetime data on earthquake occurrences, J. Comput. Graph. Stat., 8, 733-748.
2. Console, R., and M. Murru (2001), A simple and testable model for earthquake clustering, J. Geophys. Res., 106, 8699-8711.
3. Console, R., M. Murru, and A. M. Lombardi (2003), Refining earthquake clustering models, J. Geophys. Res., 108(B10), 2468, doi:10.1029/ 2002JB002130.
4. Daley, D., and D. Vere-Jones (2002), An Introduction to the Theory of Point Process, vol. 1, Springer-Verlag, New York.
5. Davis, S. D., and C. Frohlich (1991), Single-link cluster analysis, synthetic earthquake catalogs, and aftershock identification, Geophys. J. Int., 104, 289-306.
6. Eggermont, P. P. B., and V. N. LaRiccia (2001), Maximum Penalized Likelihood Estimation, vol 1, Density Estimation, Springer-Verlag, New York.
7. Frohlich, C., and S. D. Davis (1990), Single-link cluster analysis as a method to evaluate spatial and temporal properties of earthquake catalogs, Geophys. J. Int., 100, 19-32, 100.
8. Gardner, J., and L. Knopoff (1974), Is the sequence of earthquakes in southern California, with aftershock removed, Poissonian?, Bull. Seismol. Soc. Am., 64, 1363-1367.
9. Helmstetter, A., and D. Sornette (2002), Subcritical and supercritical regimes in epidemic models of earthquake aftershocks, J. Geophys. Res., 107(B10), 2237, doi:10.1029/2001JB001580.
10. Helmstetter, A., and D. Sornette (2003), Importance of direct and indirect triggered seismicity in the ETAS model of seismicity, Geophys. Res. Lett., 30(11), 1576, doi:10.1029/2003GL017670.
11. Helmstetter, A., G. Ouillon, and D. Sornette (2003), Are aftershocks of large California earthquakes diffusing?, J. Geophys. Res., 108(B10), 2483, doi:10.1029/2003JB002503.
12. Ikeya, M., and Q. Huang (1997), Earthquake frequency and moment magnitude relations for mainshocks, foreshocks and aftershocks: Theoretical b values, Episodes, 20, 181-184.
13. Kagan, Y. Y. (1991), Likelihood analysis of earthquake catalogues, Geophys. J. Int., 106, 135-148.
14. Kagan, Y., and L. Knopoff (1976), Statistical search for non-random features of the seismicity of strong earthquakes, Phys. Earth Planet. Inter., 12, 291-318.
15. Kagan, Y. Y., and F. P. Schoenberg (2001), Estimation of the upper cutoff parameter for the tapered Pareto distribution, J. Appl. Probab., 38A, 158-175.
16. Kanamori, H., and D. Anderson (1975), Theoretical basis of some empirical relations in Seismology, Bull. Seismol. Soc. Am., 65, 1073-1095.
17. Keilis-Borok, V. I., and V. I. Kossobokov (1986), Time of increased probability for the great earthquakes of the world, Comput. Seismol., 19, 45-58.
18. Legrand, D. (2002), Fractal dimensions of small, intermediate and large earthquakes, Bull. Seismol. Soc. Am., 92, 3318-3320.
19. Lewis, P. A. W., and E. Shedler (1979), Simulation of non-homogeneous Poisson processes by thinning, Naval Res. Logistics Q., 26, 403-413.
20. Musmeci, F., and D. Vere-Jones (1986), A variable-grid algorithm for smoothing clustered data, Biometrics, 42, 483-494.
21. Musmeci, F., and D. Vere-Jones (1992), A space-time clustering model for historical earthquakes, Ann. Inst. Stat. Math., 44, 1-11.
22. Ogata, Y. (1981), On Lewis' simulation method for point processes, IEEE Transl. Inf. Theory, IT-27, 23-31.
23. Ogata, Y. (1988), Statistical models for earthquake occurrences and residual analysis for point processes, J. Am. Stat. Assoc., 83, 9-27.
24. Ogata, Y. (1998), Space-time point-process models for earthquake occurrences, Ann. Inst. Stat. Math., 50, 379-402.
25. Ogata, Y. (1999), Seismicity analyses through point-process modelling: A review, Pure Appl. Geophys., 155, 471-507.
26. Ogata, Y., K. Katsura, and M. Tanemura (2003), Modelling heterogeneous space-time occurrences of earthquake and its residual analysis, J. R. Stat. Soc. Appl. Stat., 52(Part 4), 499-509.
27. Omori, F. (1894), On after-shocks of earthquakes, J. Coll. Sci. Imp. Univ. Tokyo, 7, 111-200.
28. Pacheco, J., C. Scholz, and L. Sykes (1992), Changes in frequency-size relationship from small to large earthquakes, Nature, 355, 71-73.
29. Rathbun, S. L. (1993), Modeling marked spatio-temporal point patterns, Bull. Int. Stat. Inst., 55(Book 2), 379-396.
30. Reasenberg, P. (1985), Second-order moment of central California seismicity, 1969-1982, J. Geophys. Res., 90(B7), 5479-5495.
31. Schoenberg, F. P. (2003), Multi-dimensional residual analysis of point process models for earthquake occurrences, J. Am. Stat. Assoc., 98(464), 789-795.
32. Shimazaki, K. (1986), Small and large earthquakes: The effect of the thickness of the seismogenic layer and the free surface, in Earthquake Source Mechanics, Geophys. Monogr. Ser., vol. 37, edited by S. Das, J. Boatwright, and C. H. Scholz, pp. 209-216, AGU, Washington, D. C.
33. Silverman, B. W. (1986), Density Estimation for Statistics and Data Analysis, Monogr. Stat. Appl. Probab., vol. 26, Chapman and Hall, New York.
34. Utsu, T. (1969), Aftershock and earthquake statistics (I): Some parameters which characterize an aftershock sequence and their interrelations, J. Fac. Sci. Hokkaido Univ., Ser. VII, 3, 129-195.
35. Utsu, T., Y. Ogata, and R. S. Matsu'ura (1995), The centenary of the Omori formula for a decay law of aftershock activity, J. Phys. Earth, 43, 1-33.
36. Vere-Jones, D. (1992), Statistical methods for the description and display of earthquake catalogues, in Statistics in the Environmental and Earth Sciences, edited by A. Walden and P. Guttorp, pp. 220-236, Edward Arnold, London.
37. Vere-Jones, D. (1995), Forecasting earthquakes and earthquake risk, Int. J. Forecasting, 11, 503-538.
38. Vere-Jones, D. (1999), Probability and information gain for earthquake forecasting, Comput. Seismol., 30, 248-263.
39. Yamanaka, Y., and K. Shimazaki (1990), Scaling relationship between the number of aftershocks and the size of the main shock, J. Phys. Earth, 38, 305-324.
40. Zhuang, J. (2000), Statistical modelling of the seismicity patterns before and after the 1990 Oct 5 Cape Palliser earthquake, New Zealand, N. Z. J. Geol. Geophys., 43, 447-460.
41. Zhuang, J. (2003), Some applications of point processes in seismicity modelling and prediction, Ph.D. thesis, Grad. Univ. of Adv. Stud., Kanagawa, Japan.
42. Zhuang, J., Y. Ogata, and D. Vere-Jones (2002), Stochastic declustering of space-time earthquake occurrences, J. Am. Stat. Assoc., 97, 369-380.